# Solving Integral of 1/(sinx)^4

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## Homework Statement

integral of 1/(sinx)^4

i dunno

## The Attempt at a Solution

ive tried substitution but that just results in a more complicated integral, integration by parts does the same thing without actually reducing the integral. I though i could use integration by parts to recreate the original integral but, i can't get that to work either. any help?

This looks like something where you would do Wierstrass substitution.
http://math.berkeley.edu/~reshetik/LN/1B-lec6.pdf [Broken]

t=tan(x/2); sin(x) = 2t/(1+t2); then figure out what dx so you can replace it with dt. After you've integrated, remember that t=tan(x/2).

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hints:

not enough?

still not enouh?

## 1. What is the basic approach to solving the integral of 1/(sinx)^4?

The basic approach to solving this integral is to use trigonometric identities and substitution to simplify the integrand, then apply integration techniques such as u-substitution or partial fractions to evaluate the integral.

## 2. Why is the integral of 1/(sinx)^4 considered difficult to solve?

The integral of 1/(sinx)^4 is considered difficult because it involves higher powers of sine and cosine functions, which can be challenging to manipulate and integrate. It also requires multiple steps and techniques to simplify the integrand and evaluate the integral.

## 3. Can the integral of 1/(sinx)^4 be solved using only basic calculus techniques?

Yes, the integral of 1/(sinx)^4 can be solved using basic calculus techniques such as substitution, integration by parts, and partial fractions. However, it may require multiple steps and careful manipulation of trigonometric identities.

## 4. Are there any special cases or restrictions when solving the integral of 1/(sinx)^4?

Yes, when solving the integral of 1/(sinx)^4, it is important to note that the integrand is undefined at certain values of x, specifically at x = 0 and x = (2n+1)π/2, where n is any integer. These values must be excluded from the domain of the integral.

## 5. How can the integral of 1/(sinx)^4 be used in real-world applications?

The integral of 1/(sinx)^4 can be used in various real-world applications, such as in physics and engineering, to calculate the energy or power in a system. It can also be used in statistics and probability to calculate the area under certain probability distributions.